University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 17 3 2026 09 01 Concentration of Ethanol and Acetaldehyde Inside the Catalyst Particle and in the Reaction Stream: Theoretical and Numerical Approach 233 253 115718 10.22052/ijmc.2026.257981.2091 EN Baskaran Yamuna Department of Mathematics‎, ‎Saraswathi Narayanan College‎, ‎Madurai-625022‎, ‎India 0009-0008-6562-4427 Athimoolam Meena Department of Mathematics‎, ‎Saraswathi Narayanan College‎, ‎Madurai-625022‎, ‎India 0000-0003-2312-6848 Lakshmanan Rajendran Department of Mathematics‎, ‎AMET Deemed to be University‎, ‎Kanathur‎, ‎Chennai‎- ‎603112‎, ‎India 0000-0002-2003-4553 Mohammad Izadi Department of Applied Mathematics‎, ‎Faculty of Mathematics and Computer‎, ‎Shahid Bahonar University of Kerman‎, ‎Kerman 76169-14111‎, ‎Iran,\\Department of Mathematics‎, ‎Saveetha School of Engineering‎, ‎SIMATS‎, ‎Saveetha University‎, ‎Chennai 602105‎, ‎Tamil Nadu‎, ‎India 0000-0002-6116-4928 Journal Article 2025 11 17 ‎The current research investigates the nonlinear behaviour of dimensionless ethanol and acetaldehyde concentrations in a fixed-bed laboratory reactor operating with a ${Mn}_9{Cu}_1$ catalyst for catalytic combustion‎. ‎The main objective is to obtain accurate analytical solutions of the coupled nonlinear governing equations and evaluate their usefulness for reactor analysis‎. ‎A semi-analytical hyperbolic function method is applied to derive rapidly convergent solutions‎, ‎which are validated through MATLAB (version 7.8.0‎, ‎R2009a) numerical simulations‎. ‎Excellent agreement between analytical and numerical results confirms the reliability of the method‎. ‎The findings show that the approach efficiently captures reactive transport and catalytic kinetics while reducing computational iteration time‎. ‎The solutions provide insight into catalyst performance and ethanol oxidation efficiency‎, ‎supporting optimization of reactor operating conditions‎. ‎Overall‎, ‎the study demonstrates that the hyperbolic function method is a simple‎, ‎computationally efficient tool for modelling complex nonlinear catalytic combustion systems‎. Catalytic combustion Nonlinear reaction kinetics Fixed-bed reactor modelling Hyperbolic function method mathematical chemistry https://ijmc.kashanu.ac.ir/article_115718_ca517f33fc250e5d8a31665ac2915c89.pdf